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How to define characteristics of Impedance in Transmission line?

Components of transmission line include wire , coaxial cables, dielectric slabs, optical fibre, electric power lines and Wave guides.

Transmission line can representedIn terms of four distributed parameters:

I) R =  Resistance per unit length

II) L =  Inductance per unit length 

III) G = Conductance per unit length

IV) C  =  Capacitance per unit length

Characteristics Impedance :-

It is defined as ratio of positively traveling voltage wave to current wave at any point online. It is also known as natural impedance.
Characteristics Impedance,

             √ R + j2πfL
Z0   =   -------------------- ohms
            √  G + j2πfC

Propagation constant of line,

Gamma (γ)= ( α ) Alpha + j(β) beta

Here α is real of propagation constant and it's measure of changes in magnitude Of current or Voltage in each section and is called attenuation constant. And β is an
Imaginary part of propagation and is the difference in phase angle between the input Current and the output Current or the corresponding voltage and is called phase shift constant.

Gamma(γ) =√ ZY = √ ( R + j2πfL ) ( G + j2πfC)

Phase velocity of propagation,

Vp = λ f   = --------
                  β ( beta)
And wavelength  λ=  -------
Characteristics impedance is fixed by the geometry of two conductors. For a parallel wire line with insulation, it is

                                      276               d
Calculated as Z0  =  ---------- log e ----
                                      √k                 r

Where  d = Distance between conductor
               r = Radius of Conductor
               k = Relative permittivity of
                     Insulation between Conductors
For a coaxial transmission line, The characteristics Impedance is calculated as

           138              d1
Z0 = --------- log e ------
           √k                d2

Where d1 = Inside diameter of outer
             d2 = Outside diameter of inner

Velocity factor of cable,

    Velocity of wave propagation
=  ----------------------------------------------
     Velocity of light in vacuum

     v         1
= ----- = ------
     c       √k

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